Do limit cycles matter in the long run? Stable orbits and sliding-mass dynamics emerge in task-optimal locomotion

摘要: We investigate the task-optimality of legged limit cycles and present numerical evidence supporting a simple general locomotion-planning template. Limit have been foundational to control analysis systems, but as robots move toward completing real-world tasks, are practical in long run? address this question both figuratively literally by solving for optimal strategies long-horizon tasks spanning many 20 running steps. These scenarios were designed embody locomotion such evading pursuer, formulated with minimal constraints (complete task, minimize energy cost, don't fall). By leveraging large-scale constrained optimization techniques, we numerically solve trajectory reduced-order model optimally complete each scenario. find, tested flat terrain, that near-limit-cycle behaviors emerge after transient period acceleration deceleration, suggesting may be useful, near-optimal planning target. On rough enforcing cycle on every step only degrades gait economy 2–5% compared 20-step look-ahead planning. When perturbing scenario single “bump” road, converged manner giving appearance an exponentially stable orbit, despite not explicitly exponential stability. Further, show periods deceleration near-optimally approximated “sliding mass” results support notion can useful approximations task-optimal behavior, thus near-term targets long-term